You need to be careful when adding a private video to collections because the privacy settings of channels, groups, showcases, and portfolios will often override the privacy settings for your individual video. To remove your video from any of the collections it's currently in, go to the General tab, Collections section in your video settings and uncheck the box next to the desired collection. Don't forget to click "Save" before leaving your video settings.
A video added through a public collection can be indexed through Google, but can only be accessed through the collection. If the video is restricted for privacy with a password, it'll only be viewable with that password. Though it may be indexed and show up in search results, the video's privacy is not overridden. (Note that protecting a video with a password is only available with paid memberships.)
Channels and Groups
The privacy settings of channels and groups will always override the privacy settings for your individual video. For example, a password-protected video added to a public channel will be accessible to anyone who views that channel.
Not all private videos can be added to channels and groups. Videos that have the privacy settings “Only people with the private link” or “Hide this video from vimeo.com” cannot be added to channels or groups, since doing so would allow the video to be discoverable on Vimeo.
If you add any of your private videos to a public showcase, the private videos in that showcase will only be visible to you (the video owner).
If you add any of your private videos to a password-protected showcase, people with access to the showcase will see the private videos after entering the showcase password unless the embed privacy of that video doesn't allow it to be shown on your Showcase's domain.
The privacy settings of portfolios will always override the privacy settings for your individual video. A private video added to a public portfolio will be accessible to anyone with the link to the portfolio. A private video added to a password-protected portfolio will be accessible to anyone with the portfolio password.
Anyone who you share your private video's review page link with will be able to see your private video, unless the video is password-protected. If your video is password-protected, anyone who you share your review page link with will need to enter the video password before they can view your review page.